kyotsu-test 2011 QII-Q1

kyotsu-test · Japan · eju-math__session1 Probability Definitions Probability Distribution and Sampling
There are nine cards on which the integers from 1 to 9 are written in a box. Two cards are taken simultaneously from this box. Let $S$ denote the sum of the numbers written on the two cards.
(1) The probability that $S$ is 5 or less is $\frac { \mathbf { A } } { \mathbf { B } }$. Let us assign a score to the result $S$.
When $S$ is 5 or less the score is $10 - S$, and when it is greater than 5 the score is 2. Then the expected value of the score is $\frac { \mathbf { C D } } { \mathbf { E F } }$.
(2) Let us perform the above trial twice, returning the two cards to the box before the second trial.
(i) The probability that $S$ is 5 or less in both trials is $\frac { \mathbf { G } } { \mathbf { H } }$.
(ii) The probability that $S$ is 5 or less in at least one trial is $\frac { \mathbf { J K } } { \mathbf { L M } }$.
There are nine cards on which the integers from 1 to 9 are written in a box. Two cards are taken simultaneously from this box. Let $S$ denote the sum of the numbers written on the two cards.

(1) The probability that $S$ is 5 or less is $\frac { \mathbf { A } } { \mathbf { B } }$. Let us assign a score to the result $S$.

When $S$ is 5 or less the score is $10 - S$, and when it is greater than 5 the score is 2. Then the expected value of the score is $\frac { \mathbf { C D } } { \mathbf { E F } }$.

(2) Let us perform the above trial twice, returning the two cards to the box before the second trial.

(i) The probability that $S$ is 5 or less in both trials is $\frac { \mathbf { G } } { \mathbf { H } }$.

(ii) The probability that $S$ is 5 or less in at least one trial is $\frac { \mathbf { J K } } { \mathbf { L M } }$.